Method for reversely deducing and designing appearance of wheel tread by using contact angle difference and rolling circle radius difference

Abstract

The invention discloses a method for backstepping and designing a wheel tread profile by using a contact angle difference and a rolling circle radius difference, and relates to a wheel tread profile design method, which comprises the following steps of: selecting a wheel tread profile conforming to basic parameters; setting an original point of a wheel tread coordinate system as a point where a rolling circle is located and an original point of a rail head coordinate system as a common tangent point of a rail surface; changing the transverse movement amount of the wheel set, and solving a wheel-rail contact point, a contact angle and a tread profile by using a trace method; obtaining a contact angle difference according to the contact angle data; taking a wheel-rail contact point when the transverse movement amount of the wheel set is 0 as an integral initial value, and respectively integrating tangent values of contact angle differences in positive and negative directions of the transverse movement amount to obtain a rolling circle radius difference curve; a wheel set rolling circle radius difference curve obtained by using a trace method is compared, and the tread appearance obtained through reverse deduction meets the requirement; and obtaining part of the wheel tread profile, checking the rolling circle radius difference curve of the wheel tread profile, and obtaining the wheel tread profile. The combined action of the whole wheel pair on the left side wheel and the right side wheel is considered, the design precision is higher, wheel rail abrasion is reduced, and the service life is prolonged.

Description

Technical Field

[0001] The invention relates to a method for designing a wheel tread profile, in particular to a method for designing a wheel tread profile by reversely deducing a contact angle difference and a rolling circle radius difference. Background Art

[0002] The design of railway wheel treads has important theoretical significance and practical value in the field of rail transportation, and is directly related to the safety, stability and economy of train operation. The wheel tread is the core component of the wheel-rail system. It not only bears the weight of the train, but also bears the lateral and longitudinal forces generated during driving and braking. With the development of railway transportation towards high speed and heavy load, the design of wheel treads faces more complex operating environments and higher performance requirements. Traditional wheel tread design methods usually rely on the combination of geometric characteristics and mechanical properties, based on engineering experience or simplified models, and are designed by optimizing single performance indicators such as curve passing performance, vehicle running stability or wear characteristics. These methods show high effectiveness under relatively simplified working conditions, but their limitations are increasingly prominent in modern high-speed and heavy-load railway operations. Wheel-rail contact behavior is the core issue in wheel tread design. The contact state between the wheel tread and the rail surface will affect the dynamic characteristics of the train, and the contact angle difference and rolling circle radius difference are two key parameters. The contact angle difference reflects the change in the relative angle between the wheel and rail surface when the wheel and rail are in contact, which has an important impact on the train's ability to negotiate curves and operating stability; the rolling circle radius difference describes the change in the rolling circle radius of the wheel-rail contact point during the lateral movement of the wheelset, which has a significant effect on the wear distribution and traction performance of the wheel. Optimizing these two parameters can not only improve the matching performance of the wheel-rail system, but also improve the dynamic performance of the train operation, reduce wear and extend the service life of the wheels and rails. However, in traditional design methods, due to insufficient understanding of the complexity of wheel-rail contact behavior, it is often difficult to effectively control the contact angle difference and rolling circle radius difference, thereby limiting the overall performance of the wheel tread design.

[0003] Related patent document: CN105512397A discloses a method for designing the tread shape of an independent wheel and an independent wheel. The tread shape design method includes the following steps: 1) determining the left and right wheel contact angle difference curves according to vehicle parameters, track parameters and the desired vehicle dynamics performance indicators; 2) giving an initial wheel-rail contact point distribution area; 3) taking the left and right wheel contact angle difference curves of step 1) and the wheel-rail contact point distribution area of ​​step 2) as the wheel tread shape design targets, and according to the relationship between the rail shape, rail bottom slope, wheel tread shape, left and right wheel contact angle difference curves and wheel-rail contact point distribution area, the wheel tread shape that meets the requirements can be inferred; 4) calculating the wheel-rail contact stress according to the designed tread shape; 5) judging whether the wheel-rail contact stress is optimal, otherwise returning to step 2) to readjust the wheel-rail contact point distribution area until the wheel-rail contact stress converges to the minimum value.

[0004] The design accuracy of the above technologies is average and needs to be improved. Summary of the invention

[0005] The purpose of the present invention is to provide a method for reversely designing the wheel tread profile using the contact angle difference and the rolling circle radius difference, which can take into account the joint effect of the left and right wheels of the entire wheelset, has higher design accuracy, effectively reduces wheel-rail wear and prolongs the service life of the wheels and rails, obtains a good wheel-rail contact geometry, and thus improves the train running stability and passenger riding comfort.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is as follows: A method for designing a wheel tread profile by reverse calculation using a contact angle difference and a rolling circle radius difference (or a method for designing a railway wheel tread profile by reverse calculation using a contact angle difference and a rolling circle radius difference), the technical solution of which is that it comprises the following steps: S1. Obtain the rail head shape and rail bottom slope of the railway rail, and select the wheel tread shape that meets the basic parameters, wherein the basic parameters include track gauge, inner distance of wheelset, wheel flange height, wheel flange thickness, wheel hub width, tread width, distance from the rolling circle point to the wheel back, distance from the wheel flange thickness measurement point to the rolling circle point, and vertical distance from the track gauge measurement point to the top surface; S2, setting the origin of the wheel tread coordinate system as the point where the rolling circle is located, and the origin of the rail head coordinate system as the common tangent point of the left and right rail surfaces; S3. Considering the influence of the wheelset roll angle, change the lateral displacement of the wheelset, and use the trace method to obtain the wheel-rail contact point, contact angle and wheel tread shape when the lateral displacement of the wheelset changes within the range of -12.5mm to 12.5mm; S4. Obtaining the contact angle difference based on the wheel-rail contact angle data on the left and right sides; S5, taking the wheel-rail contact point when the wheelset lateral displacement is 0 as the initial value of integration, integrating the tangent value of the contact angle difference in the positive and negative directions of the lateral displacement respectively, and obtaining a rolling circle radius difference curve based on the contact angle difference; S6. Compare the wheelset rolling circle radius difference curve obtained by the trace method with the wheelset rolling circle radius difference curve based on the contact angle difference. When the difference between the two values ​​under the same lateral displacement is less than the set value, it is determined that the rolling circle radius difference value based on the contact angle difference is within an acceptable range, that is, the tread shape obtained by reverse deduction meets the requirements of the engineering design. Otherwise, the tread shape needs to be adjusted and redesigned. S7, obtaining a part of the wheel tread profile, checking the rolling circle radius difference curve (i.e. checking the rolling circle radius difference curve of the part of the wheel tread profile), and obtaining a wheel tread profile that meets certain contact angle difference curve and rolling circle radius difference curve requirements; S8. Based on the newly obtained wheel tread shape, perform contact characteristic calculation and contact stress analysis, and perform smoothing and other processing as needed.

[0007] Among the above technical solutions, the preferred technical solution may be that in step S1, the following method is used to set: the wheels and rails included in the above wheel-rail are rigid, that is, the elastic deformation of the wheel-rail contact is negligible; the rail head shape is convex, that is, the tangent slope of each point changes monotonically; the rail head shape and the designed wheel tread shape are bilaterally symmetrical; the given wheel flange height, wheel flange thickness and tread width remain unchanged. In step S3, the wheel-rail contact point, contact angle and wheel tread shape are obtained in the following manner: S31. Given the rail head shape and the target tread shape (i.e., the "seed" tread shape), considering the effect of the wheelset side roll angle, the condition for calculating the contact angle is: ; ; ; ; ; ; ; ; ; ; in, The rail head shape; is the target tread profile; is the rolling angle of the wheelset; is the lateral displacement of the wheelset; the coordinates of the contact points between the left wheel tread and the rail surface are and , the coordinates of the contact points between the right wheel tread and the rail surface are and ; and The left and right contact angles, respectively.

[0008] S32. Calculate the ordinate of the tread shape using the contact angle. After obtaining the contact angle, the following expression is obtained through transformation: ; ; in, is the ordinate of the tread shape; Indicates the vertical coordinate of the tread contact point when the lateral displacement is 0.

[0009] In the above technical solution, a preferred technical solution may also be that in step S4, the contact angle difference is calculated using the following formula: ;in, is the contact angle difference.

[0010] In the above technical solution, a preferred technical solution may also be that in step S5, the rolling circle radius difference calculation formula based on the contact angle difference is as follows: ; in, is the rolling circle radius difference calculated based on the contact angle difference; when the wheelset lateral displacement is 0, .

[0011] In the above technical solution, a preferred technical solution may also be that step S6 includes: S61, using a trace method, obtaining a wheelset rolling circle radius difference curve through the side tread profile curves of the left and right wheels; S62, obtaining a wheelset rolling circle radius difference curve obtained based on the contact angle difference; S63. Compare the two above curves and calculate the following formula: ; in, is the wheelset rolling circle radius difference obtained by the trace method; is the wheelset rolling circle radius difference obtained by the trace method; is the set error value, .

[0012] If the above formula does not hold, Adjust the designed tread, distribute the part corresponding to the lateral displacement less than 0 to the left wheel, and the rest to the right wheel, and compare it with the original tread parameter, that is, the rolling circle radius difference.

[0013] In the above technical solutions, a preferred technical solution may also be that the redesign in step S6 refers to repeating step S6 and comparing with the original wheel tread parameters.

[0014] In the above technical solution, a preferred technical solution may also be that step S7 includes: S71, obtaining a partial wheel tread profile, and checking whether a rolling circle radius difference curve (of the partial wheel tread profile) differs from an expected curve based on the obtained partial wheel tread profile. value, is the set error value, , then the newly obtained part of the wheel tread shape is expanded according to the original wheel tread shape, and the expansion principle is to ensure that the basic parameters of the wheel tread remain unchanged; S72, refine the step length of the wheelset lateral displacement to improve the calculation accuracy; S73, directly changing the shape of the local line of the curve, and calculating a new tread shape, so as to obtain a wheel tread shape that meets the requirements of a certain contact angle difference curve and a rolling circle radius difference curve; S74. The new tread shape needs to be merged to obtain a complete wheel tread shape.

[0015] In the modern railway operation environment, the train running speed increases, the load increases, and the curve radius decreases. These factors cause the wheel-rail contact behavior to show obvious nonlinear and complex dynamic characteristics. Based on the reverse design method of contact angle difference and rolling circle radius difference, the wheel tread shape is optimized by geometric and mechanical calculations of the wheelset. Different from the traditional design path, this method directly integrates the optimization target of the wheel-rail contact relationship on the left and right sides of the entire wheelset into the design process, and uses the mapping relationship between contact parameters and tread geometry to reversely solve the tread shape that meets the target performance. The reverse design considering the wheelset structure provides a new technical path for the rail transit field, which helps to promote the transformation of wheel tread design theory from geometric and mechanical static design based on a single wheel-rail to dynamic optimization based on the comprehensive contact behavior of wheelset-rail. Therefore, at the current stage of rapid development of rail transit technology, studying and promoting wheel tread reverse design technology is not only of great significance to improving the comprehensive performance of the wheel-rail system, but also will provide strong technical support for the continuous improvement of the manufacturing level of rail transit equipment. In view of this, the present invention proposes a method for reversely designing the railway wheel tread profile using the contact angle difference and the rolling circle radius difference to design and optimize the wheel tread profile curve, thereby improving the train running stability and passenger riding comfort.

[0016] The beneficial effects of the above technical solution of the present invention are: By optimizing the contact behavior of the wheelset as a whole rather than a single wheel, the present invention can more comprehensively consider the dynamic coordination of the left and right wheels, thereby improving the stability of the wheelset when passing through curves. The coordinated optimization of the difference in contact angle and rolling circle radius between the left and right wheels effectively reduces the asymmetric force distribution between the wheel and rail, avoiding lateral deviation and safety hazards during vehicle operation.

[0017] Based on the design of the entire wheelset, the dynamic offset of the wheel-rail contact point and its adaptability to track gauge changes can be more accurately controlled, reducing the excitation phenomenon and body vibration during vehicle operation. By coordinating the rolling circle radius difference between the left and right wheels, the asymmetric torque during wheel operation is reduced, significantly improving the smoothness of train operation and the comfort experience of passengers.

[0018] The traditional method only considers a single wheel, which cannot avoid the difference in contact conditions between the left and right wheels during operation, resulting in uneven wheel-rail wear and shortened service life. By considering the contact behavior of the entire wheelset, the present invention effectively balances the friction force distribution between the wheel and rail, reduces local wear, and extends the service life of the wheel and rail, thereby significantly reducing maintenance costs and track maintenance frequency.

[0019] The present invention is suitable for optimizing wheel-rail contact under complex working conditions such as high speed, heavy load and small curve radius. By dynamically optimizing the entire wheelset, comprehensive adaptation to multiple working conditions can be achieved, improving the operational reliability and performance stability of the rail transit system under harsh conditions. The design method provided by the present invention takes into account the joint action of the left and right wheels of the entire wheelset, with higher design accuracy, effectively improving the stability of the wheels during operation, and improving the performance and operational economy of the rail transit system.

[0020] In addition, the present invention breaks through the traditional idea of ​​single wheel optimization and provides a new technical path for the overall design of wheelsets. This method can not only be directly applied to wheel tread design, but also provide theoretical and methodological support for the dynamic analysis and optimization of more complex wheel-rail systems.

[0021] The present invention provides a method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference. The method takes into account the joint action of the left and right wheels of the entire wheelset, has higher design accuracy, effectively reduces wheel-rail wear and prolongs the service life of the wheels and rails, obtains a good wheel-rail contact geometric relationship, and thus improves the stability of train operation and the riding comfort of passengers. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 The figure is a schematic diagram of the process of reverse design of railway wheel tread profile in the present invention.

[0023] Figure 2 , Figure 3 is a schematic diagram of the wheel-rail contact point pair. Figure 2 The left side is a schematic diagram of the wheel-rail contact point pair. Figure 3 Schematic diagram of the wheel-rail contact point pair on the right.

[0024] Figure 4 , Figure 5 is the curve of the wheel-rail contact parameters on the left and right sides changing with the lateral displacement, Figure 4 is the curve of the difference in wheel-rail contact angle between the left and right sides as a function of the lateral displacement, Figure 5 This is the curve showing the difference in rolling circle radius between the left and right wheels and the amount of lateral displacement.

[0025] Figure 6 , Figure 7 is the curve of the integral of the contact angle tangent value versus the lateral displacement, Figure 6 is the wheel-rail corresponding curve on the left side, Figure 7 This is the corresponding curve for the wheel-rail on the right.

[0026] Figure 8 It is the curve of the difference in rolling circle radius between the left and right wheel rails versus the lateral displacement, including the original tread and the designed tread 1.

[0027] Fig. 9 It is the curve of the relative error value of the rolling circle radius difference between the designed tread 1 and the original tread as the lateral displacement changes.

[0028] Fig.10 , Fig.11 is the curve of the change of the integral of the contact angle tangent value with the lateral displacement after correction according to the relative error value of the rolling circle radius difference. Fig.10 is the corresponding curve of the left wheel-rail, Fig.11 is the corresponding curve of the wheel-rail on the right.

[0029] Fig.12 It is the curve showing the difference in rolling circle radius between the left and right wheel rails after correction as a function of the lateral displacement, including the original tread and the designed tread 2.

[0030] Fig.13 This is the curve showing the change of the relative error value of the rolling circle radius difference between the corrected designed tread 2 and the original tread as the lateral displacement increases.

[0031] Fig.14 , Fig.15 is the curve of the integral of the contact angle tangent value versus the lateral displacement after secondary correction based on the relative error value of the rolling circle radius difference. Fig.14 is the corresponding curve of the left wheel-rail, Fig.15 is the corresponding curve of the wheel-rail on the right.

[0032] Fig.16 It is the curve of the difference in rolling circle radius between the left and right wheel rails after secondary correction versus lateral displacement, including the original tread and the designed tread 3 (the two curves almost overlap).

[0033] Fig.17 It is the variation curve of the relative error value of the rolling circle radius difference between the designed tread 3 and the original tread after secondary correction with the lateral displacement.

[0034] Fig.18 , Fig.19 is the curve of the integral of the contact angle tangent value after smoothing and second correction versus the lateral displacement. Fig.18 is the corresponding curve of the left wheel-rail (the two curves almost overlap), Fig.19 is the corresponding curve of the wheel-rail on the right side (the two curves almost coincide).

[0035] Fig. 20 , Fig.21 This is a comparison of the final designed wheel tread shape and the original wheel tread shape. Fig. 20 is the corresponding curve of the left wheel-rail, Fig.21 is the corresponding curve of the wheel-rail on the right. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described in conjunction with the embodiments below. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on this embodiment, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of the present invention.

[0037] Example 1: Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Fig. 9 , Fig.10 , Fig.11 , Fig.12 , Fig.13 , Fig.14 , Fig.15 , Fig.16 , Fig.17 , Fig.18 , Fig.19 , Fig. 20 , Fig.21 As shown, the method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference of the present invention comprises the following steps: S1. Obtain the rail head shape and rail bottom slope of the railway rail, and select the wheel tread shape that meets the basic parameters, where the basic parameters include track gauge, inner distance of wheelset, wheel flange height, wheel flange thickness, wheel hub width, tread width, distance from the rolling circle point to the wheel back, distance from the wheel flange thickness measurement point to the rolling circle point, and vertical distance from the track gauge measurement point to the top surface. In step S1, the following method is used for setting: the wheels and rails contained in the above wheel rail are rigid, that is, the elastic deformation of the wheel-rail contact is negligible; the rail head shape is convex, that is, the tangent slope of each point changes monotonically; the rail head shape and the designed wheel tread shape are bilaterally symmetrical; the given wheel flange height, wheel flange thickness and tread width remain unchanged. The selected railway rail head shape is CN60, the rail bottom slope is 1 / 40, and the track gauge is 1435 mm; the wheel tread shape is LM, the nominal rolling circle radius of the wheel is 420 mm, the inner distance of the wheel back is 1353 mm, the step length of the wheelset lateral displacement is 0.05 mm, and the calculation range of the wheelset lateral displacement is -12.5~12.5 mm.

[0038] S2. Set the origin of the wheel tread coordinate system to the point where the rolling circle is located, and the origin of the rail head coordinate system to the common tangent point of the left and right rail surfaces.

[0039] S3, considering the influence of the wheelset roll angle, changing the lateral displacement of the wheelset, and using the trace method to obtain the wheel-rail contact point, contact angle and wheel tread shape when the lateral displacement of the wheelset changes within the range of -12.5mm to 12.5mm. That is, in step S3, the wheel-rail contact point, contact angle and wheel tread shape are obtained in the following manner: S31. Given the rail head shape and the target tread shape (i.e., the "seed" tread shape), that is, for the CN60 rail head shape and the LM wheel tread shape, considering the effect of the wheelset side roll angle, the condition for calculating the contact angle is: ; ; ; ; ; ; ; ; ; ; in, The rail head shape; is the target tread profile; is the rolling angle of the wheelset; is the lateral displacement of the wheelset; the coordinates of the contact points between the left wheel tread and the rail surface are and , the coordinates of the contact points between the right wheel tread and the rail surface are and ; and The left and right contact angles, respectively.

[0040] S32. Calculate the ordinate of the tread shape using the contact angle. After obtaining the contact angle, the following expression is obtained through transformation: ; ; in, is the ordinate of the tread shape; The vertical coordinate of the tread contact point when the lateral displacement is 0 is 420mm.

[0041] S4. According to the left and right wheel-rail contact angle data, the contact angle difference is obtained. In step S4, the formula for calculating the contact angle difference is as follows: ;in, is the contact angle difference.

[0042] S5. Taking the wheel-rail contact point when the wheelset lateral displacement is 0 as the initial value of integration, integrate the tangent value of the contact angle difference in the positive and negative directions of the lateral displacement respectively to obtain a rolling circle radius difference curve based on the contact angle difference.

[0043] In step S5, the rolling circle radius difference calculation formula based on the contact angle difference is as follows: ; in, is the rolling circle radius difference calculated based on the contact angle difference; when the wheelset lateral displacement is 0, During the calculation process, the integration step size was set to 0.05 mm.

[0044] S6. Compare the wheelset rolling circle radius difference curve obtained by the trace method and the wheelset rolling circle radius difference curve based on the contact angle difference. When the difference between the two values ​​under the same lateral displacement is less than the set value, it is determined that the rolling circle radius difference value based on the contact angle difference is within an acceptable range, that is, the tread shape obtained by reverse deduction meets the requirements of engineering design. Otherwise, the tread shape needs to be adjusted and redesigned; the redesign in step S6 refers to repeating step S6 and comparing with the original wheel tread parameters. Step S6 includes: S61, using a trace method, obtaining a wheelset rolling circle radius difference curve through the side tread profile curves of the left and right wheels; S62, obtaining a wheelset rolling circle radius difference curve obtained based on the contact angle difference; S63. Compare the two above curves and calculate the following formula: ;in, is the wheelset rolling circle radius difference obtained by the trace method; is the set error value, .

[0045] If the above formula does not hold, Adjust the designed tread, distribute the part corresponding to the lateral displacement less than 0 to the left wheel, and the rest to the right wheel, and compare it with the original tread parameter, that is, the rolling circle radius difference.

[0046] S7, obtaining a part of the wheel tread profile, checking the rolling circle radius difference curve (of the part of the wheel tread profile), and obtaining a wheel tread profile that meets certain contact angle difference curve and rolling circle radius difference curve requirements. Step S7 includes: S71, obtaining a partial wheel tread profile, and checking whether a rolling circle radius difference curve (of the partial wheel tread profile) differs from an expected curve based on the obtained partial wheel tread profile. value, is the set error value, , then the newly obtained part of the wheel tread shape is expanded according to the original wheel tread shape, and the expansion principle is to ensure that the basic parameters of the wheel tread remain unchanged; S72, refine the step length of the wheelset lateral displacement to improve the calculation accuracy; S73, directly changing the shape of the local line of the curve, and calculating a new tread shape, so as to obtain a wheel tread shape that meets the requirements of a certain contact angle difference curve and a rolling circle radius difference curve; S74. The new tread shape needs to be merged to obtain a complete wheel tread shape.

[0047] Since some sections of the new tread profile do not contact the rail surface, when the tread is reversely designed based on the contact angle difference and rolling circle radius difference, the non-contact area of ​​the tread cannot be designed, so it needs to be combined with the reference tread to form a complete wheel tread profile. The reversely designed tread consists of the reference tread, the designed tread, and the transition section between the two.

[0048] S8. Based on the newly obtained wheel tread shape, perform contact characteristic calculation and contact stress analysis, and perform smoothing and other processing as needed.

[0049] The present invention compares the new design tread with the original LM tread: The present invention verifies the effectiveness of the design method by comparing the standard LM wheel tread and the wheel tread designed by reverse calculation based on the contact angle difference and rolling circle radius difference method (defined as design treads 1 to 3). The curve of the difference in rolling circle radius between the left and right sides of the standard LM wheel tread and the reversely designed wheel tread versus the lateral displacement is shown in Figure 2. Figure 8 , Fig.12 and Fig.16 It can be seen that within the range of -12.5 to 12.5 mm of lateral displacement, the curve of the difference in rolling circle radius between the left and right sides of the wheel tread designed by reverse calculation and the lateral displacement is consistent with the corresponding curve of the standard LM wheel tread after two corrections, indicating that the designed wheel tread meets the design requirements after two corrections.

[0050] Further, according to Fig. 9 and Fig.13 The curve of the relative error of the rolling circle radius difference on the left and right sides with the lateral displacement is shown, and the curve of the integral of the tangent value of the contact angle on the left and right sides with the lateral displacement after the first and second corrections (design tread 2 and design tread 3) is obtained, as shown in Fig.10 , Fig.11 , Fig.14 and Fig.15 By comparing the rolling circle radius difference between the designed tread 3 and the original tread, as shown in Fig.16 As shown, the corresponding relative error curve of the rolling circle radius difference on the left and right sides is drawn, as shown in Fig.17 As shown, the relative error is less than 10 -6 Therefore, the designed shape of tread 3 meets the requirements of engineering design. Fig.18 , Fig.19 It is the integral curve of the tangent value of the left and right contact angles after smoothing, that is, the curve of the change of the shape of the designed tread 3 with the lateral displacement. Fig. 20 , Fig.21 The figure is a comparison of the final designed left and right wheel tread shapes and the original left and right wheel tread shapes.

[0051] contrast Figure 2 , Figure 3 and Fig.14 , Fig.15 , we can get that the error of the designed tread 3 relative to the original tread in the ordinate direction is less than 0.0035 mm; at the same time, Fig. 20 , Fig.21 The wheel tread shape of the final design is very close to the original wheel tread shape; thus, it is shown that the wheel tread reverse design method proposed by the present invention meets the requirements of engineering design. If the accuracy needs to be further improved, it can be obtained by adjusting the above lateral displacement calculation step length.

[0052] Traditional wheel tread design methods often focus on a single wheel, ignoring the dynamic interaction of the entire wheelset as a system during track operation. This limitation makes it difficult to coordinate the contact behavior of the left and right wheels, thus affecting the stability and safety of the train. The design technology using overall wheelset optimization can fully consider the synergy between the left and right wheels, and make the contact behavior of the entire wheelset more balanced by optimizing the contact angle difference and rolling circle radius difference. This optimization can not only improve the curve performance of the train and enhance the anti-roll stability, but also improve the train's adaptability under complex conditions such as high speed, heavy load and small curve radius, significantly improving the safety and reliability of train operation.

[0053] The development of rail transit is facing an increasing demand for energy conservation and sustainable development. The uneven wear of the wheel-rail system not only shortens the service life of wheels and rails, but also significantly increases maintenance costs and operating burdens. The technical solution of the present invention can effectively reduce local wear and wear differences by optimizing the contact behavior of the wheelset as a whole, thereby extending the service life of the wheel-rail system, thereby reducing the frequency of maintenance and replacement, and directly reducing operating costs. In addition, the technical solution can also improve wheel-rail matching, reduce wheel-rail friction energy consumption, and provide technical support for energy conservation and consumption reduction in rail transit.

[0054] From the perspective of theoretical research, the technical solution of the present invention breaks the traditional idea of ​​single wheel optimization by introducing the reverse design of overall wheelset optimization in tread design. This not only deepens the understanding of wheel-rail contact behavior, but also provides new technical support for multi-objective dynamic optimization problems, which can be further applied to multi-scale dynamic analysis, intelligent optimization design, and research and development of rail transportation equipment in the field of rail transportation.

[0055] Compared with the technical solution disclosed in CN105512397A (reference document 1), the present invention adopts the contact angle difference curve and the wheel-rail contact distribution function as the design objective function, thereby using the wheel-rail geometric constraint model to reversely infer the tread shape of the contact section. The present invention first uses the contact angle difference curve to obtain the rolling circle radius difference curve, and then compares the rolling circle radius difference curve obtained by the trace method with the rolling circle radius difference curve based on the contact angle difference. When the difference between the two values ​​under the same lateral displacement is less than the set value, it is considered that the rolling circle radius difference value based on the contact angle difference is within an acceptable range, that is, the tread shape obtained by reverse inference meets the requirements. Therefore, the difference is that the objective function of the present invention is the rolling circle radius difference curve (that is, the present invention also considers the rolling circle radius difference verification). Compared with the technical effect produced by the present invention in reference document 1, the present invention adds the rolling circle radius difference verification on the basis of using the contact angle difference to reverse the tread shape. Therefore, the present invention has higher design accuracy, the design accuracy is improved by more than 10%, and the stability of the wheel during operation is effectively improved.

[0056] In summary, the above embodiments of the present invention provide a method for reversely designing the wheel tread profile using the contact angle difference and the rolling circle radius difference. This method takes into account the joint action of the left and right wheels of the entire wheelset, has higher design accuracy, effectively reduces wheel-rail wear and extends the service life of wheels and rails, obtains a good wheel-rail contact geometry, and thus improves the stability of train operation and passenger comfort.

Claims

1. A method for designing the wheel tread profile by reverse calculation using the contact angle difference and the rolling circle radius difference, characterized in that: It includes the following steps: S1. Obtain the rail head shape and rail bottom slope of the railway rail, and select the wheel tread shape that meets the basic parameters, wherein the basic parameters include track gauge, inner distance of wheelset, wheel flange height, wheel flange thickness, wheel hub width, tread width, distance from the rolling circle point to the wheel back, distance from the wheel flange thickness measurement point to the rolling circle point, and vertical distance from the track gauge measurement point to the top surface; S2, setting the origin of the wheel tread coordinate system as the point where the rolling circle is located, and the origin of the rail head coordinate system as the common tangent point of the left and right rail surfaces; S3. Considering the influence of the wheelset roll angle, change the lateral displacement of the wheelset, and use the trace method to obtain the wheel-rail contact point, contact angle and wheel tread shape when the lateral displacement of the wheelset changes within the range of -12.5mm to 12.5mm; S4. Obtaining the contact angle difference based on the wheel-rail contact angle data on the left and right sides; S5, taking the wheel-rail contact point when the wheelset lateral displacement is 0 as the initial value of integration, integrating the tangent value of the contact angle difference in the positive and negative directions of the lateral displacement respectively, and obtaining a rolling circle radius difference curve based on the contact angle difference; S6. Compare the wheelset rolling circle radius difference curve obtained by the trace method with the wheelset rolling circle radius difference curve based on the contact angle difference. When the difference between the two values ​​under the same lateral displacement is less than the set value, it is determined that the rolling circle radius difference value based on the contact angle difference is within an acceptable range, that is, the tread shape obtained by reverse deduction meets the requirements of the engineering design. Otherwise, the tread shape needs to be adjusted and redesigned. S7, obtaining a part of the wheel tread profile, checking the rolling circle radius difference curve, and obtaining a wheel tread profile that meets certain contact angle difference curve and rolling circle radius difference curve requirements; S8. For the newly obtained wheel tread shape, perform contact characteristic calculation and contact stress analysis, and perform smoothing as needed.

2. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: In step S1, the following method is used to set: The wheels and rails included in the above-mentioned wheel-rail are rigid, that is, the elastic deformation of the wheel-rail contact is negligible; the rail head shape is convex, that is, the tangent slope of each point changes monotonically; the rail head shape and the designed wheel tread shape are symmetrical on the left and right; the given wheel flange height, wheel flange thickness and tread width remain unchanged.

3. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: In step S3, the wheel-rail contact point, contact angle and wheel tread profile are obtained in the following manner: S31. Given the rail head shape and target tread shape, considering the effect of the wheelset roll angle, the condition for calculating the contact angle is: ； ； ； ； ； ； ； ； ； ； in, The rail head shape; is the target tread profile; is the rolling angle of the wheelset; is the lateral displacement of the wheelset; the coordinates of the contact points between the left wheel tread and the rail surface are and , the coordinates of the contact points between the right wheel tread and the rail surface are and ; and The left and right contact angles, respectively; S32. Calculate the ordinate of the tread shape using the contact angle. After obtaining the contact angle, the following expression is obtained through transformation: ； ； in, is the ordinate of the tread shape; Indicates the vertical coordinate of the tread contact point when the lateral displacement is 0.

4. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: In step S4, the contact angle difference is calculated as follows: ;in, is the contact angle difference.

5. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: In step S5, the rolling circle radius difference calculation formula based on the contact angle difference is as follows: ;in, is the rolling circle radius difference calculated based on the contact angle difference; when the wheelset lateral displacement is 0, .

6. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: Step S6 includes: S61, using a trace method, obtaining a wheelset rolling circle radius difference curve through the side tread profile curves of the left and right wheels; S62, obtaining a wheelset rolling circle radius difference curve obtained based on the contact angle difference; S63. Compare the two above curves and calculate the following formula: ； in, is the wheelset rolling circle radius difference obtained by the trace method; is the set error value, ; If the above formula does not hold, according to Adjust the designed tread, distribute the part corresponding to the lateral displacement less than 0 to the left wheel, and the rest to the right wheel, and compare it with the original tread parameter, that is, the rolling circle radius difference.

7. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: The redesign in step S6 refers to repeating step S6 and comparing with the original wheel tread parameters.

8. The method for reversely designing the wheel tread profile by using the contact angle difference and the rolling circle radius difference according to claim 1, characterized in that: Step S7 includes: S71, obtaining a partial wheel tread profile, and checking whether the rolling circle radius difference curve thereof differs from the expected curve according to the obtained partial wheel tread profile value, is the set error value, , then the newly obtained part of the wheel tread shape is expanded according to the original wheel tread shape, and the expansion principle is to ensure that the basic parameters of the wheel tread remain unchanged; S72, refining the step length of the wheelset lateral displacement change; S73, directly changing the shape of the local lines of the curve to deduce the new tread shape; S74. The new tread shape needs to be merged to obtain a complete wheel tread shape.

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